There are many ways you can prevent your players from playing together. The most obvious and brute-force way is to send them all to different servers and never let them see each other again. But there are other ways to prevent players from playing together, ways that permeate even the games made by the most well-meaning of developers.
Take, for example, Rift, Trion's first MMORPG. Trion has a strong community focus, ranging from the usual "letter from the producer" feedback to more personalized GM interventions to promote in-game camaraderie. Trion also works hard to get people playing with their friends. Its Ascend-a-Friend referral program, in addition to handing out a free trial, also automatically adds referrer and referee to each others' friends lists, making it easier to find each other in-game, and giving them the ability to teleport to one another. But as Isabelle Parsley of MMORPG.com points out, this doesn't actually let them play together, because new players start at level 1 and most referring players are at level 50.
I experienced this when I invited a friend to play Rift. I was level 50, doing 50 stuff, and he was starting out at 1, so I made a new character to accompany him.
And it was going well, but sometimes he'd log in while I was in the middle of 50 stuff, and he'd level up ahead of my alt, so I'd have to level up my alt to get caught back up again, until he got so far ahead of my alt I just waited until he leveled up enough to catch up to another one of my alts, which then kind of teamed up with him again for a bit...
Long story short, he quit before he got to 50, since he never "really" got to play with me.
Rift is also trying another tactic that hasn't worked well in other games: the capped level endless trial. World of Warcraft lost nearly 20 percent of its subscribers despite implementing an endless free trial up to level 20. Warhammer Online saw players cancelling their subscriptions to play in the free trial because that was where all the PVP action was. And Lego Universe had to shut down when it found it was unable to convert free trial users into subscribers.
The problem with level capped free trials? It doesn't let people play together. Oh, sure, it technically allows them to cross paths, and subscribers could technically make low-level alts to play with free trial players. But the reality is that most subscribers are going to be higher level than the free trial level cap and they'll never have any incentive, let alone opportunity, to play with them. Left on their own, free trial players are basically playing a single player game, and then asked if they want to sign up for a subscription to this single player game. It won't work. It can't.
It is possible to design a game with "letting players play together" in mind. The most important issue is to overcome segregation barriers: the factors that completely prevent players from playing together. There are two kinds of segregation barriers: operational barriers and design barriers. Operational barriers refer to elements of the game that concern the game's operation and are largely unaffected by a player's game experience. A subscription fee is an example of an operational barrier; so is being on different servers.
Eliminating multiple servers (ala EVE Online) or allowing players to freely transfer from one server to another (ala Rift) are good examples of overcoming that barrier. Charging a fee for a server transfer or denying server transfers at all is a bad way of overcoming that barrier. This is because the operating barrier is often perceived by players in opposition to their goals.
Design barriers are trickier: they're elements of the game that separate players. These are often desirable elements in a game, such as levels, because they give players a sense of accomplishment, of going someplace they couldn't before. Getting enough gear to be able to face the bosses in a challenging raid is an example of a design barrier. So is being on the right stage of an epic quest to enter a particular dungeon.
But design barriers are also being challenged by game designers: games that offer players the ability to "mentor" "sidekick" or "level sync" overcomes the barrier presented to players of different levels, for example, and easily obtainable "welfare epics" allow games to distribute enough gear to get players into higher tier raids after lower tier raids have been abandoned.